Known in the art is an apparatus for arresting an internal combustion engine for the purpose of fuel conservation. An inherent disadvantage of the known apparatus is that it causes engine stoppage without consideration of important engine criteria, for example without establishing a minimum speed above which the engine is not stopped and further without considering the charging level of the vehicle battery which is critically important for deciding whether it is prudent to stop the engine inasmuch as it may be difficult or impossible to be restarted. Furthermore, the known apparatus fails to include provisions which prevent repeated engine stoppage at very low vehicle speeds. None of the known apparatus is able to provide for a sensitive adaptation to prevailing conditions of the vehicle and in particular tends to shut off the engine when this is counter to the driver's desires or, again, fails to shut off the engine under conditions where it would be justifiable to do so.